The interior-point revolution in constrained optimization

Interior methods are a central, striking feature of the constrained optimization landscape today, but it was not always so. Primarily in the form of barrier methods, interior-point techniques were widely used during the 1960s to solve nonlinearly constrained problems. However, their use for linear programming was not even contemplated because of the total dominance of the simplex method. During the 1970s, barrier methods were superseded by newly emerging, apparently more efficient alternatives such as augmented Lagrangian and sequential quadratic programming methods. By the early 1980s, barrier methods were almost universally regarded as a closed chapter in the history of optimization.

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